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A spectral formulation of the boundary integral equation method for antiplane problems is presented. The boundary integral equation method relates the slip and the shear stress at an interface between two half-planes. It involves evaluating a space-time convolution of the shear stress or the slip at the interface. In the spectral formulation, the convolution with respect to the spatial coordinate is performed in the spectral domain. This leads to greater numerical efficiency. Prior work on the spectral formulation of the boundary integral equation method has performed the elastodynamic convolution of the slip at the interface. In the present work, the convolution is performed of the shear stress at the interface. The spectral formulation is developed both for an interface between identical solids and for a bi-material interface. It is validated by numerically calculating the response of the interface to harmonic and to impulsive disturbances and comparing with known analytical solutions. To illustrate use of the method, dynamic slip rupture propagation with a slip-weakening friction law is simulated.

Automation and robotisation of the agricultural sector are seen as a viable solution to socio-economic challenges faced by this industry. This technology often relies on intelligent perception systems providing information about crops, plants and the entire environment. The challenges faced by traditional 2D vision systems can be addressed by modern 3D vision systems which enable straightforward localisation of objects, size and shape estimation, or handling of occlusions. So far, the use of 3D sensing was mainly limited to indoor or structured environments. In this paper, we evaluate modern sensing technologies including stereo and time-of-flight cameras for 3D perception of shape in agriculture and study their usability for segmenting out soft fruit from background based on their shape. To that end, we propose a novel 3D deep neural network which exploits the organised nature of information originating from the camera-based 3D sensors. We demonstrate the superior performance and efficiency of the proposed architecture compared to the state-of-the-art 3D networks. Through a simulated study, we also show the potential of the 3D sensing paradigm for object segmentation in agriculture and provide insights and analysis of what shape quality is needed and expected for further analysis of crops. The results of this work should encourage researchers and companies to develop more accurate and robust 3D sensing technologies to assure their wider adoption in practical agricultural applications.

We consider Broyden's method and some accelerated schemes for nonlinear equations having a strongly regular singularity of first order with a one-dimensional nullspace. Our two main results are as follows. First, we show that the use of a preceding Newton-like step ensures convergence for starting points in a starlike domain with density 1. This extends the domain of convergence of these methods significantly. Second, we establish that the matrix updates of Broyden's method converge q-linearly with the same asymptotic factor as the iterates. This contributes to the long-standing question whether the Broyden matrices converge by showing that this is indeed the case for the setting at hand. Furthermore, we prove that the Broyden directions violate uniform linear independence, which implies that existing results for convergence of the Broyden matrices cannot be applied. Numerical experiments of high precision confirm the enlarged domain of convergence, the q-linear convergence of the matrix updates, and the lack of uniform linear independence. In addition, they suggest that these results can be extended to singularities of higher order and that Broyden's method can converge r-linearly without converging q-linearly. The underlying code is freely available.

We address the problem of fitting 3D human models to 3D scans of dressed humans. Classical methods optimize both the data-to-model correspondences and the human model parameters (pose and shape), but are reliable only when initialized close to the solution. Some methods initialize the optimization based on fully supervised correspondence predictors, which is not differentiable end-to-end, and can only process a single scan at a time. Our main contribution is LoopReg, an end-to-end learning framework to register a corpus of scans to a common 3D human model. The key idea is to create a self-supervised loop. A backward map, parameterized by a Neural Network, predicts the correspondence from every scan point to the surface of the human model. A forward map, parameterized by a human model, transforms the corresponding points back to the scan based on the model parameters (pose and shape), thus closing the loop. Formulating this closed loop is not straightforward because it is not trivial to force the output of the NN to be on the surface of the human model - outside this surface the human model is not even defined. To this end, we propose two key innovations. First, we define the canonical surface implicitly as the zero level set of a distance field in R3, which in contrast to morecommon UV parameterizations, does not require cutting the surface, does not have discontinuities, and does not induce distortion. Second, we diffuse the human model to the 3D domain R3. This allows to map the NN predictions forward,even when they slightly deviate from the zero level set. Results demonstrate that we can train LoopRegmainly self-supervised - following a supervised warm-start, the model becomes increasingly more accurate as additional unlabelled raw scans are processed. Our code and pre-trained models can be downloaded for research.

We consider a biochemical model that consists of a system of partial differential equations based on reaction terms and subject to non--homogeneous Dirichlet boundary conditions. The model is discretised using the gradient discretisation method (GDM) which is a framework covering a large class of conforming and non conforming schemes. Under classical regularity assumptions on the exact solutions, the GDM enables us to establish the existence of the model solutions in a weak sense, and strong convergence for the approximate solution and its approximate gradient. Numerical test employing a finite volume method is presented to demonstrate the behaviour of the solutions to the model.

The API economy refers to the widespread integration of API (advanced programming interface) microservices, where software applications can communicate with each other, as a crucial element in business models and functions. The number of possible ways in which such a system could be used is huge. It is thus desirable to monitor the usage patterns and identify when the system is used in a way that was never used before. This provides a warning to the system analysts and they can ensure uninterrupted operation of the system. In this work we analyze both histograms and call graph of API usage to determine if the usage patterns of the system has shifted. We compare the application of nonparametric statistical and Bayesian sequential analysis to the problem. This is done in a way that overcomes the issue of repeated statistical tests and insures statistical significance of the alerts. The technique was simulated and tested and proven effective in detecting the drift in various scenarios. We also mention modifications to the technique to decrease its memory so that it can respond more quickly when the distribution drift occurs at a delay from when monitoring begins.

This paper investigates the impact of COVID-19 on financial markets. It focuses on the evolution of the market efficiency, using two efficiency indicators: the Hurst exponent and the memory parameter of a fractional L\'evy-stable motion. The second approach combines, in the same model of dynamic, an alpha-stable distribution and a dependence structure between price returns. We provide a dynamic estimation method for the two efficiency indicators. This method introduces a free parameter, the discount factor, which we select so as to get the best alpha-stable density forecasts for observed price returns. The application to stock indices during the COVID-19 crisis shows a strong loss of efficiency for US indices. On the opposite, Asian and Australian indices seem less affected and the inefficiency of these markets during the COVID-19 crisis is even questionable.

Graph Convolutional Network (GCN) has been widely applied in transportation demand prediction due to its excellent ability to capture non-Euclidean spatial dependence among station-level or regional transportation demands. However, in most of the existing research, the graph convolution was implemented on a heuristically generated adjacency matrix, which could neither reflect the real spatial relationships of stations accurately, nor capture the multi-level spatial dependence of demands adaptively. To cope with the above problems, this paper provides a novel graph convolutional network for transportation demand prediction. Firstly, a novel graph convolution architecture is proposed, which has different adjacency matrices in different layers and all the adjacency matrices are self-learned during the training process. Secondly, a layer-wise coupling mechanism is provided, which associates the upper-level adjacency matrix with the lower-level one. It also reduces the scale of parameters in our model. Lastly, a unitary network is constructed to give the final prediction result by integrating the hidden spatial states with gated recurrent unit, which could capture the multi-level spatial dependence and temporal dynamics simultaneously. Experiments have been conducted on two real-world datasets, NYC Citi Bike and NYC Taxi, and the results demonstrate the superiority of our model over the state-of-the-art ones.

Machine learning (ML) has shown to advance the research field of quantum chemistry in almost any possible direction and has recently also entered the excited states to investigate the multifaceted photochemistry of molecules. In this paper, we pursue two goals: i) We show how ML can be used to model permanent dipole moments for excited states and transition dipole moments by adapting the charge model of [Chem. Sci., 2017, 8, 6924-6935], which was originally proposed for the permanent dipole moment vector of the electronic ground state. ii) We investigate the transferability of our excited-state ML models in chemical space, i.e., whether an ML model can predict properties of molecules that it has never been trained on and whether it can learn the different excited states of two molecules simultaneously. To this aim, we employ and extend our previously reported SchNarc approach for excited-state ML. We calculate UV absorption spectra from excited-state energies and transition dipole moments as well as electrostatic potentials from latent charges inferred by the ML model of the permanent dipole moment vectors. We train our ML models on CH$_2$NH$_2^+$ and C$_2$H$_4$, while predictions are carried out for these molecules and additionally for CHNH$_2$, CH$_2$NH, and C$_2$H$_5^+$. The results indicate that transferability is possible for the excited states.